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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Mie–Gruneisen equation of state ： ウィキペディア英語版 Mie–Gruneisen equation of state The Mie-Grüneisen equation of state is a relation between the pressure and the volume of a solid at a given temperature.〔Roberts, J. K., & Miller, A. R. (1954). Heat and thermodynamics (Vol. 4). Interscience Publishers.〕〔Burshtein, A. I. (2008). Introduction to thermodynamics and kinetic theory of matter. Wiley-VCH.〕 It is used to determine the pressure in a shock-compressed solid. The Mie-Grüneisen relation is a special form of the Grüneisen model which describes the effect that changing the volume of a crystal lattice has on its vibrational properties. Several variations of the Mie–Grüneisen equation of state are in use. The Grüneisen model can be expressed in the form :$\backslash Gamma\; =\; V\; \backslash left(\backslash frac\backslash right)\_V$ where ''V'' is the volume, ''p'' is the pressure, ''e'' is the internal energy, and ''Γ'' is the Grüneisen parameter which represents the thermal pressure from a set of vibrating atoms. If we assume that ''Γ'' is independent of ''p'' and ''e'', we can integrate Grüneisen's model to get :$$ p - p_0 = \frac (e - e_0) where ''p''0 and ''e''0 are the pressure and internal energy at a reference state usually assumed to be the state at which the temperature is 0K. In that case ''p''0 and ''e''0 are independent of temperature and the values of these quantities can be estimated from the Hugoniot equations. The Mie-Grüneisen equation of state is a special form of the above equation. == History == Gustav Mie, in 1903, developed an intermolecular potential for deriving high-temperature equations of state of solids.〔Mie, G. (1903) "Zur kinetischen Theorie der einatomigen Körper." Annalen der Physik 316.8, p. 657-697.〕 In 1912 Eduard Grüneisen extended Mie's model to temperatures below the Debye temperature at which quantum effects become important.〔Grüneisen, E. (1912). Theorie des festen Zustandes einatomiger Elemente. Annalen der Physik, 344(12), 257-306.〕 Grüneisen's form of the equations is more convenient and has become the usual starting point for deriving Mie-Grüneisen equations of state.〔Lemons, D. S., & Lund, C. M. (1999). Thermodynamics of high temperature, Mie–Gruneisen solids. American Journal of Physics, 67, 1105.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Mie–Gruneisen equation of state」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.